Communication systems use various modulation and multiplexing techniques for communicating signals from a transmitter to a receiver. Multicarrier modulations, such as orthogonal frequency division multiplexing (OFDM), have been used due to advantages of improved bandwidth efficiency and data throughput over, for examples, the mobile radio channel. OFDM is an effective technique to mitigate the effects of delay spread introduced by the mobile radio channels. OFDM provides high spectral efficiency by adopting the orthogonal subcarriers and reduces the effects of intersymbol interference (ISI) by inserting the guard time between symbols to accommodate the delay spread caused by multipath.
Due to the advantages of improving bandwidth efficiency and data throughput over fading dispersive channels, OFDM has been used in many new digital wireless applications including digital video broadcasting, digital audio broadcasting, and wireless local area networks. The OFDM technique has also been proposed for a new third generation wireless systems. One of the major disadvantages of such a multicarrier modulated system is the performance sensitivity to frequency offsets. A frequency offset can result from a Doppler shift due to the mobile environment as well as from a carrier frequency synchronization error. Such a frequency offset causes a loss of the carrier orthogonality, and hence, self-introduced intercarrier interference (ICI). ICI, due to frequency offsets, affects the performance of OFDM communication systems.
In an OFDM system, the input binary data stream is firstly mapped to a signal constellation of M-ary phase shifted keying modulation or M-ary quadrature amplitude modulation. Regardless of the modulation scheme used, the mapped symbols can be represented by a series of complex numbers in vector space. Then, N complex numbers are grouped together and in turn amplitude modulated onto N orthogonal subcarriers. These N modulated subcarriers are combined to form a composite signal called an OFDM symbol. The duration TOFDM for an OFDM symbol is N·Ts where Ts is the data symbol time duration. The mapping, grouping, amplitude modulation, and combining processes continues for every N data symbols of complex numbers. Each input M-ary data stream is communicated by frequency division across the frequency bandwidth of the communication channel. On the receiver side, OFDM symbols are frequency demodulated using the same N subcarriers. At the end of each OFDM symbol, the magnitude of a complex value associated with each of the N subcarriers will be extracted. These N complex numbers are placed in sequential order and the M-ary data is recovered based on the signal constellation mapping. It is well known that the discrete Fourier transforms (DFT) can be used to realize the orthogonal frequency modulation. Also, the forward fast Fourier transform (FFT) is an effective way to implement the DFTs.
Referring to FIGS. 1A and 1B, a conventional OFDM transmitter, shown as a module, and a conventional OFDM receiver, also shown as a module, form a conventional OFDM communication system. The transmitter includes an inverse FFT (IFFT) and the receiver includes an FFT. In the conventional OFDM transmitter, a serial-to-parallel operation and a mapping operation essentially perform the grouping of N consecutive data symbols into N parallel inputs to IFFT. The IFFT will take time to complete the inverse transform operation, which essentially puts N parallel inputs to N orthogonal subcarriers. After the IFFT operation, N symbols are serialized by a parallel-to-serial operation with an equal-time spacing between consecutive samples of the IFFT output sequence. The output sequence is transmitted using conventional digital-to-analog conversion and high power amplification, not shown. The reverse operations to the transmitter occur in the receiver. The existing forward and inverse transforms of the conventional OFDM system is given by a transmitter baseband IFFT equation and a receiver baseband FFT equation.
The IFFT employed at the transmitter is defined by the transmitter baseband IFFT equation.
                              x          k                =                              ∑                          n              =              0                                      N              -              1                                ⁢                                    d              n                        ⁢                          ⅇ                              j                ⁢                                                                  ⁢                                                      2                    ⁢                    π                                    N                                ⁢                nk                                                                                                              k          =          0                ,        1        ,        2        ,        …        ⁢                                  ,                  N          -          1                    
In the transmitter baseband IFFT equation, dn is the sequence of input data symbols, k is the output symbol index, N is the number of subcarriers, xk is the output of the IFFT transmitter. After the IFFT transmitter output xk is communicated over an additive white Gaussian noise (AWGN) channel, the received signal is rk=xk+wk where wk is the channel AWGN. The FFT employed at the receiver is defined by the receiver baseband FFT equation.
                                          d            ^                    k                =                              1            N                    ⁢                                    ∑                              n                =                0                                            N                -                1                                      ⁢                                          r                n                            ⁢                              ⅇ                                                      -                    j                                    ⁢                                                                          ⁢                                                            2                      ⁢                      π                                        N                                    ⁢                  nk                                                                                                                              k          =          0                ,        1        ,        2        ,        …        ⁢                                  ,                  N          -          1                    
In the receiver baseband FFT equation, {circumflex over (d)}k is the output of the FFT receiver as the estimated transmitter input data symbol, and N is the number of subcarriers. In order to maintain orthogonality without crosstalk among the subcarriers at the receiver, two conditions must be satisfied, that is, the demodulating carriers need to be exactly aligned with the transmitted carriers, and the receiver demodulation process takes place over a period of time exactly equal to the reciprocal of the subcarrier spacing Δf. If either of these conditions does not exist, the orthogonality is no longer perfectly maintained and the intercarrier interference (ICI), or, crosstalk, is self-generated. One of the major disadvantages of an OFDM system is the sensitivity of performance to a frequency offset. The frequency offset can result from a Doppler shift due to mobile environment as well as from a carrier frequency synchronization error. Such a frequency offset causes a loss of subcarrier orthogonality, and hence, self-introduced ICI. As a result, the desired signal is distorted and the bit-error-rate (BER) performance is degraded.
An OFDM signal is a composite signal of N component signals, modulated on N orthogonal subcarriers. The desired component signal should ideally be only on the desired subcarrier of interest. In the presence of frequency offset, the signal strength at any desired subcarrier will be reduced and the signal will leak into other undesired subcarriers, meaning that there exists ICI from a subcarrier to other subcarriers, at the output of the FFT receiver. Without losing generality, the desired component signal is on the subcarrier with an index zero for the FFT operation. Referring to all of the Figures, and particularly to FIG. 2, a weighting factor is defined as the square root of the percentage of the signal power, located on a particular subcarrier, that leaks to each of the other undesired subcarriers. When there is no frequency offset, the weighting factor should be 1.0 at the subcarrier index zero, and the weighting factor should be zero for all other indices. For weighting factors of a 16-point FFT with a frequency offset of 0.2·Δf, the weighting factor on the desired signal is less than 1 and those on other undesired sub-carriers are greater than 0. These non-zero weighting factors represent ICI. Practically, there is a limitation on the frequency offset that an OFDM receiver can tolerate. Such limitations for a 16-QAM OFDM system is 4% or less of Δf. Conventional systems have a 4% frequency offset limitation of the intercarrier frequency spacing when N=16.
The existing architecture of OFDM includes a transmitter, and using an inverse transform function, communicating with a receiver using a forward transform function. These paired transform functions are well known to have a limitation on the frequency offset that the receiver can tolerate within acceptable performance expectations. This performance limitation results from signal distortion due to the intercarrier interference when the frequency offset exists. These and other disadvantages are solved or reduced using the invention.